A finite population model of mlecular evolution: theory and computation

This article is concerned with the evolution of haploid organisms that reproduce asexually. In a seminal piece of work, Eigen and coauthors proposed the quasispecies model in an attempt to understand such an evolutionary process. Their work has impacted antiviral treatment and vaccine design strategies. Yet, predictions of the quasispecies model are at best viewed as a guideline, primarily because it assumes an infinite population size, whereas realistic population sizes can be quite small. In this paper we consider a population genetics-based model aimed at understanding the evolution of such organisms with finite population sizes and present a rigorous study of the convergence and computational issues that arise therein. Our first result is structural and shows that, at any time during the evolution, as the population size tends to infinity, the distribution of genomes predicted by our model converges to that predicted by the quasispecies model. This justifies the continued use of the quasispecies model to derive guidelines for intervention. While the stationary state in the quasispecies model is readily obtained, due to the explosion of the state space in our model, exact computations are prohibitive. Our second set of results are computational in nature and address this issue. We derive conditions on the parameters of evolution under which our stochastic model mixes rapidly. Further, for a class of widely used fitness landscapes we give a fast deterministic algorithm which computes the stationary distribution of our model. These computational tools are expected to serve as a framework for the modeling of strategies for the deployment of mutagenic drugs.

Feedback Overhead-Aware, Distributed, Fast, and Reliable Selection

In a communication system in which K nodes communicate with a central sink node, the following problem of selection often occurs. Each node maintains a preference number called a metric, which is not known to other nodes. The sink node must find the `best' node with the largest metric. The local nature of the metrics requires the selection process to be distributed. Further, the selection needs to be fast in order to increase the fraction of time available for data transmission using the selected node and to handle time-varying environments. While several selection schemes have been proposed in the literature, each has its own shortcomings. We propose a novel, distributed selection scheme that generalizes the best features of the timer scheme, which requires minimal feedback but does not guarantee successful selection, and the splitting scheme, which requires more feedback but guarantees successful selection. The proposed scheme introduces several new ideas into the design of the timer and splitting schemes. It explicitly accounts for feedback overheads and guarantees selection of the best node. We analyze and optimize the performance of the scheme and show that it is scalable, reliable, and fast. We also present new insights about the optimal timer scheme.

Secure Computation in a Bidirectional Relay

Bidirectional relaying, where a relay helps two user nodes to exchange equal length binary messages, has been an active area of recent research. A popular strategy involves a modified Gaussian MAC, where the relay decodes the XOR of the two messages using the naturally-occurring sum of symbols simultaneously transmitted by user nodes. In this work, we consider the Gaussian MAC in bidirectional relaying with an additional secrecy constraint for protection against a honest but curious relay. The constraint is that, while the relay should decode the XOR, it should be fully ignorant of the individual messages of the users. We exploit the symbol addition that occurs in a Gaussian MAC to design explicit strategies that achieve perfect independence between the received symbols and individual transmitted messages. Our results actually hold for a more general scenario where the messages at the two user nodes come from a finite Abelian group G, and the relay must decode the sum within G of the two messages. We provide a lattice coding strategy and study optimal rate versus average power trade-offs for asymptotically large dimensions.

Fast Likelihood Computation in Speech Recognition using Matrices

Acoustic modeling using mixtures of multivariate Gaussians is the prevalent approach for many speech processing problems. Computing likelihoods against a large set of Gaussians is required as a part of many speech processing systems and it is the computationally dominant phase for Large Vocabulary Continuous Speech Recognition (LVCSR) systems. We express the likelihood computation as a multiplication of matrices representing augmented feature vectors and Gaussian parameters. The computational gain of this approach over traditional methods is by exploiting the structure of these matrices and efficient implementation of their multiplication. In particular, we explore direct low-rank approximation of the Gaussian parameter matrix and indirect derivation of low-rank factors of the Gaussian parameter matrix by optimum approximation of the likelihood matrix. We show that both the methods lead to similar speedups but the latter leads to far lesser impact on the recognition accuracy. Experiments on 1,138 work vocabulary RM1 task and 6,224 word vocabulary TIMIT task using Sphinx 3.7 system show that, for a typical case the matrix multiplication based approach leads to overall speedup of 46 % on RM1 task and 115 % for TIMIT task. Our low-rank approximation methods provide a way for trading off recognition accuracy for a further increase in computational performance extending overall speedups up to 61 % for RM1 and 119 % for TIMIT for an increase of word error rate (WER) from 3.2 to 3.5 % for RM1 and for no increase in WER for TIMIT. We also express pairwise Euclidean distance computation phase in Dynamic Time Warping (DTW) in terms of matrix multiplication leading to saving of approximately of computational operations. In our experiments using efficient implementation of matrix multiplication, this leads to a speedup of 5.6 in computing the pairwise Euclidean distances and overall speedup up to 3.25 for DTW.

Design and analysis of a peer-to-peer based distributed clock synchronisation protocol for wireless sensor networks

Clock synchronisation is an important requirement for various applications in wireless sensor networks (WSNs). Most of the existing clock synchronisation protocols for WSNs use some hierarchical structure that introduces an extra overhead due to the dynamic nature of WSNs. Besides, it is difficult to integrate these clock synchronisation protocols with sleep scheduling scheme, which is a major technique to conserve energy. In this paper, we propose a fully distributed peer-to-peer based clock synchronisation protocol, named Distributed Clock Synchronisation Protocol (DCSP), using a novel technique of pullback for complete sensor networks. The pullback technique ensures that synchronisation phases of any pair of clocks always overlap. We have derived an exact expression for a bound on maximum synchronisation error in the DCSP protocol, and simulation study verifies that it is indeed less than the computed upper bound. Experimental study using a few TelosB motes also verifies that the pullback occurs as predicted.

Distributed Space Time Coding for Wireless Two-Way Relaying

We consider the wireless two-way relay channel, in which two-way data transfer takes place between the end nodes with the help of a relay. For the Denoise-And-Forward (DNF) protocol, it was shown by Koike-Akino et al. that adaptively changing the network coding map used at the relay greatly reduces the impact of Multiple Access Interference at the relay. The harmful effect of the deep channel fade conditions can be effectively mitigated by proper choice of these network coding maps at the relay. Alternatively, in this paper we propose a Distributed Space Time Coding (DSTC) scheme, which effectively removes most of the deep fade channel conditions at the transmitting nodes itself without any CSIT and without any need to adaptively change the network coding map used at the relay. It is shown that the deep fades occur when the channel fade coefficient vector falls in a finite number of vector subspaces of, which are referred to as the singular fade subspaces. DSTC design criterion referred to as the singularity minimization criterion under which the number of such vector subspaces are minimized is obtained. Also, a criterion to maximize the coding gain of the DSTC is obtained. Explicit low decoding complexity DSTC designs which satisfy the singularity minimization criterion and maximize the coding gain for QAM and PSK signal sets are provided. Simulation results show that at high Signal to Noise Ratio, the DSTC scheme provides large gains when compared to the conventional Exclusive OR network code and performs better than the adaptive network coding scheme.

Information-theoretically secure regenerating codes for distributed storage

Regenerating codes are a class of codes for distributed storage networks that provide reliability and availability of data, and also perform efficient node repair. Another important aspect of a distributed storage network is its security. In this paper, we consider a threat model where an eavesdropper may gain access to the data stored in a subset of the storage nodes, and possibly also, to the data downloaded during repair of some nodes. We provide explicit constructions of regenerating codes that achieve information-theoretic secrecy capacity in this setting.

A Savitzky-Golay Filtering Perspective of Dynamic Feature Computation

We address the classical problem of delta feature computation, and interpret the operation involved in terms of Savitzky- Golay (SG) filtering. Features such as themel-frequency cepstral coefficients (MFCCs), obtained based on short-time spectra of the speech signal, are commonly used in speech recognition tasks. In order to incorporate the dynamics of speech, auxiliary delta and delta-delta features, which are computed as temporal derivatives of the original features, are used. Typically, the delta features are computed in a smooth fashion using local least-squares (LS) polynomial fitting on each feature vector component trajectory. In the light of the original work of Savitzky and Golay, and a recent article by Schafer in IEEE Signal Processing Magazine, we interpret the dynamic feature vector computation for arbitrary derivative orders as SG filtering with a fixed impulse response. This filtering equivalence brings in significantly lower latency with no loss in accuracy, as validated by results on a TIMIT phoneme recognition task. The SG filters involved in dynamic parameter computation can be viewed as modulation filters, proposed by Hermansky.

Feedback overhead-aware fast distributed selection scheme for multi-node wireless systems

Opportunistic selection is a practically appealing technique that is used in multi-node wireless systems to maximize throughput, implement proportional fairness, etc. However, selection is challenging since the information about a node's channel gains is often available only locally at each node and not centrally. We propose a novel multiple access-based distributed selection scheme that generalizes the best features of the timer scheme, which requires minimal feedback but does not always guarantee successful selection, and the fast splitting scheme, which requires more feedback but guarantees successful selection. The proposed scheme's design explicitly accounts for feedback time overheads unlike the conventional splitting scheme and guarantees selection of the user with the highest metric unlike the timer scheme. We analyze and minimize the average time including feedback required by the scheme to select. With feedback overheads, the proposed scheme is scalable and considerably faster than several schemes proposed in the literature. Furthermore, the gains increase as the feedback overhead increases.

Fast acoustic likelihood computation using low-rank matrix approximation

Acoustic modeling using mixtures of multivariate Gaussians is the prevalent approach for many speech processing problems. Computing likelihoods against a large set of Gaussians is required as a part of many speech processing systems and it is the computationally dominant phase for LVCSR systems. We express the likelihood computation as a multiplication of matrices representing augmented feature vectors and Gaussian parameters. The computational gain of this approach over traditional methods is by exploiting the structure of these matrices and efficient implementation of their multiplication.In particular, we explore direct low-rank approximation of the Gaussian parameter matrix and indirect derivation of low-rank factors of the Gaussian parameter matrix by optimum approximation of the likelihood matrix. We show that both the methods lead to similar speedups but the latter leads to far lesser impact on the recognition accuracy. Experiments on a 1138 word vocabulary RM1 task using Sphinx 3.7 system show that, for a typical case the matrix multiplication approach leads to overall speedup of 46%. Both the low-rank approximation methods increase the speedup to around 60%, with the former method increasing the word error rate (WER) from 3.2% to 6.6%, while the latter increases the WER from 3.2% to 3.5%.

Novel algorithms for distributed sequential hypothesis testing

This paper considers sequential hypothesis testing in a decentralized framework. We start with two simple decentralized sequential hypothesis testing algorithms. One of which is later proved to be asymptotically Bayes optimal. We also consider composite versions of decentralized sequential hypothesis testing. A novel nonparametric version for decentralized sequential hypothesis testing using universal source coding theory is developed. Finally we design a simple decentralized multihypothesis sequential detection algorithm.

Enabling node repair in any erasure code for distributed storage

Erasure codes are an efficient means of storing data across a network in comparison to data replication, as they tend to reduce the amount of data stored in the network and offer increased resilience in the presence of node failures. The codes perform poorly though, when repair of a failed node is called for, as they typically require the entire file to be downloaded to repair a failed node. A new class of erasure codes, termed as regenerating codes were recently introduced, that do much better in this respect. However, given the variety of efficient erasure codes available in the literature, there is considerable interest in the construction of coding schemes that would enable traditional erasure codes to be used, while retaining the feature that only a fraction of the data need be downloaded for node repair. In this paper, we present a simple, yet powerful, framework that does precisely this. Under this framework, the nodes are partitioned into two types and encoded using two codes in a manner that reduces the problem of node-repair to that of erasure-decoding of the constituent codes. Depending upon the choice of the two codes, the framework can be used to avail one or more of the following advantages: simultaneous minimization of storage space and repair-bandwidth, low complexity of operation, fewer disk reads at helper nodes during repair, and error detection and correction.

Distributed STBCs with full-diversity partial interference cancellation decoding

Recently, Guo and Xia introduced low complexity decoders called Partial Interference Cancellation (PIC) and PIC with Successive Interference Cancellation (PIC-SIC), which include the Zero Forcing (ZF) and ZF-SIC receivers as special cases, for point-to-point MIMO channels. In this paper, we show that PIC and PIC-SIC decoders are capable of achieving the full cooperative diversity available in wireless relay networks. We give sufficient conditions for a Distributed Space-Time Block Code (DSTBC) to achieve full diversity with PIC and PIC-SIC decoders and construct a new class of DSTBCs with low complexity full-diversity PIC-SIC decoding using complex orthogonal designs. The new class of codes includes a number of known full-diversity PIC/PIC-SIC decodable Space-Time Block Codes (STBCs) constructed for point-to-point channels as special cases. The proposed DSTBCs achieve higher rates (in complex symbols per channel use) than the multigroup ML decodable DSTBCs available in the literature. Simulation results show that the proposed codes have better bit error rate performance than the best known low complexity, full-diversity DSTBCs.

Enabling node repair in any erasure code for distributed storage

Erasure codes are an efficient means of storing data across a network in comparison to data replication, as they tend to reduce the amount of data stored in the network and offer increased resilience in the presence of node failures. The codes perform poorly though, when repair of a failed node is called for, as they typically require the entire file to be downloaded to repair a failed node. A new class of erasure codes, termed as regenerating codes were recently introduced, that do much better in this respect. However, given the variety of efficient erasure codes available in the literature, there is considerable interest in the construction of coding schemes that would enable traditional erasure codes to be used, while retaining the feature that only a fraction of the data need be downloaded for node repair. In this paper, we present a simple, yet powerful, framework that does precisely this. Under this framework, the nodes are partitioned into two types and encoded using two codes in a manner that reduces the problem of node-repair to that of erasure-decoding of the constituent codes. Depending upon the choice of the two codes, the framework can be used to avail one or more of the following advantages: simultaneous minimization of storage space and repair-bandwidth, low complexity of operation, fewer disk reads at helper nodes during repair, and error detection and correction.

Cooperative distributed sequential spectrum sensing

We consider cooperative spectrum sensing for cognitive radios. We develop an energy efficient detector with low detection delay using sequential hypothesis testing. Sequential Probability Ratio Test (SPRT) is used at both the local nodes and the fusion center. We also analyse the performance of this algorithm and compare with the simulations. Modelling uncertainties in the distribution parameters are considered. Slow fading with and without perfect channel state information at the cognitive radios is taken into account.